In the figure given below, ABC is a right angled , isoceles triangle .

Question

In the figure given below, ABC is a right angled , isoceles triangle . If BC||DE, BC =x and DE =y, what is the area of the plot of DBCE?

chetan2u · Answer

riangle ADE and  	riangle ABC  are right angled , isoceles triangles... 
So Area of  	riangle ADE=\frac{1}{2}*AD*DE=\frac{y*y}{2}=\frac{y^2}{2}  and Area of  	riangle ABC=\frac{1}{2}*AB*BC=\frac{1}{2}*x*x=\frac{x^2}{2}

The area of the plot of DBCE=Area of  	riangle ADE  - Area of  	riangle ABC  =  \frac{x^2-y^2}{2}

aalam383 · Answer

Can you tell me how did we know ADE is a isosceles triangle? Thanks!

CEO2021 · Answer

aalam383 question does not mentions the part " DE parallel to BC" above solution assumed the same.... else other fine!!!!!

patrapan · Answer

if DE parallel to BC then option A else might be other option

chikonali · Answer

It's a problem of similar triangle.Think the properties of similar triangle & find the solution on your own.

here BC=X & DE=Y
Since ABC is an isosceles triangle, side AC is represented by 90 degree, side AB & BC both are represented by 45 degree.

In triangle ADE,side AE is represented by 90 degree and both AD & DE are by 45 degree.

So we can write, BC=AB=X
 DE=AD=Y
So the area of triangle ADE is
1/2(AD*DE)=1/2(Y*Y)=(Y^2)/2
and area of ABC =1/2(AB*BC)
 =1/2(X*X)=(X^2)/2
So now area of DBCE= - 
=(X^2-Y^2)/2
Answer:A

Posted from my mobile device

harshpathak96 · Answer

chetan2u 
 Bunuel 
 KarishmaB

the question doesn't mention that DE is parallel to BC, so how do we infer that the two triangles are similar? I think without that information the answer should be E.

chetan2u · Answer

You are correct, it is not specifically mentioned. It should have been given accordingly.

But answer cannot be E, as ‘none of these’ means there is some answer possible, which is not given in option.

However, if the lines are not parallel, then the answer cannot be determined.

In the figure given below, ABC is a right angled , isoceles triangle .

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GMAT Problem Solving (PS) Questions

In the figure given below, ABC is a right angled , isoceles triangle .

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